M.C.Q (1 Marks) - Page 4 - MATHS STD 11 Science Questions - Vidyadip

Questions · Page 4 of 4

M.C.Q (1 Marks)

MCQ 1511 Mark

Which of the following is a statement?

A
Today is Monday
B
Tomorrow will be holiday
✓
If today is Tuesday then tomorrow will be Sunday
D
There will be full moon tonight

Answer

Correct option: C.

If today is Tuesday then tomorrow will be Sunday

“Today is Monday”, “Tomorrow will be holiday”, “There will be full moon tonight” are not the statements because we are not sure which day or night we are talking about.
“If today is Tuesday then tomorrow will be Sunday” is a statement because we are sure that it is false.
Wednesday come after Tuesday so if today is Tuesday then tomorrow will be Wednesday.

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MCQ 1521 Mark

Find the truth value of the compound statement, $4$ is the first composite number and $2 + 5 = 7.$

✓
$T$
B
$F$
C
Neither $T$ nor $F$
D
Cannot be determined

Answer

Correct option: A.

$T$

The given statement is True, as $4$ is the first composite number.
Also $2 + 5 = 7$

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MCQ 1531 Mark

The only statement among the following that is a tautology is.

A
$A ∧ (A ∨ B)$
B
$A ∨ (A ∧ B)$
✓
$[A ∧ (A \rightarrow B)] \rightarrow B$
D
$B \rightarrow [A ∧ (A \rightarrow B)]$

Answer

Correct option: C.

$[A ∧ (A \rightarrow B)] \rightarrow B$

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MCQ 1541 Mark

Which of the following statement is false?

A
$24$ is even number or odd number
B
$15$ is prime or divisible by $3$
C
$71$ is odd number or prime
✓
Japan or China is in India

Answer

Correct option: D.

Japan or China is in India

$24$ is even number so $“24$ is even number or odd number” is correct.
$15$ is divisible by $3$ so $“15$ is prime or divisible by $3”$ is true.
$71$ is prime as well as odd so $“71$ is odd number or prime” is true.
Neither Japan nor China is in India so “Japan or China is in India” is false.

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MCQ 1551 Mark

The contrapositive of the statement If $p$ then $q$ is:

A
If $q$, then $p.$
B
If $p,$ then $\sim q.$
✓
If $\sim q,$ then $\sim p.$
D
If $\sim p,$ then $ \sim q.$

Answer

Correct option: C.

If $\sim q,$ then $\sim p.$

The contrapositive of the statement If $p,$ then $q,$ is If $\sim q,$ then $\sim p.$

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MCQ 1561 Mark

Let $p$ and $q$ be two propositions. Then the contrapositive of the implication $p \rightarrow q$ is.

✓
$\sim q \rightarrow \sim p$
B
$\sim p \rightarrow \sim q$
C
$\sim q \rightarrow p$
D
$p \rightarrow q$

Answer

Correct option: A.

$\sim q \rightarrow \sim p$

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MCQ 1571 Mark

The converse of the statement if a number is divisible by $10,$ then it is divisible by $5$ is.

A
If a number is not divisible by $5,$ then it is not divisible by $10$
B
If a number is divisible by $5,$ then it is not divisible by $10$
C
If a number is not divisible by $5,$ then it is divisible by $10$
✓
If a number is divisible by $5,$ then it is divisible by $10$

Answer

Correct option: D.

If a number is divisible by $5,$ then it is divisible by $10$

Given, statement is if a number is divisible by $10,$ then it is divisible by $5$
Now, converse of the statement is:
If a number is divisible by $5,$ then it is divisible by $10$

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MCQ 1581 Mark

Choose the correct answer:
The negation of the statement.
“Rajesh or Rajni lived in Bangalore” is.

A
Rajesh did not live in Bangalore or Rajni lives in Bangalore.
B
Rajesh lives in Bangalore and Rajni did not live in Bangalore.
✓
Rajesh did not live in Bangalore and Rajni did not live in Bangalore.
D
Rajesh did not live in Bangalore or Rajni did not live in Bangalore.

Answer

Correct option: C.

Rajesh did not live in Bangalore and Rajni did not live in Bangalore.

We have, $p:$ Rajesh or Rajni lived in Bangalore.
and $q:$ Rajesh lived in Bangalore.
$r:$ Rajni lived in Bangalore.
$\sim q:$ Rajesh did not live in Bangalore.
$\sim r.$ Rajni did not live in Bangalore.
$\sim (q v r):$ Rajesh did not live in Bangalore and Rajni did not live in Bangalore.

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MCQ 1591 Mark

Which is logically equivalent to "If today is Sunday Matt cannot play hockey"?

A
Today is Sunday and Matt can play hockey.
✓
If Matt plays hockey then today is not Sunday.
C
Today is Sunday and Matt cannot play hockey.
D
Today is not Sunday if and only if Matt plays hockey.

Answer

Correct option: B.

If Matt plays hockey then today is not Sunday.

Matt can play Hockey on any day other than Sunday.

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MCQ 1601 Mark

If $p \Rightarrow (\text{q ∨ r})$ is false, then the truth values of $\text{p, q, r,}$ are respectively.

✓
$\text{T, F, F}$
B
$\text{F, F, F}$
C
$\text{F, T, T}$
D
$\text{T, T, F}$

Answer

Correct option: A.

$\text{T, F, F}$

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MCQ 1611 Mark

Which of the following is not a statement?

A
$2$ is an even integer.
B
$2 + 1= 3.$
C
The number $17$ is prime.
✓
$x + 3 = 10, x Î R.$

Answer

Correct option: D.

$x + 3 = 10, x Î R.$

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MCQ 1621 Mark

The connective in the statement $2 + 7 > 9$ or $2 + 7 < 9$ is.

A
And
✓
Or
C
$ > $
D
$ < $

Answer

Correct option: B.

Or

Given, statement is $2 + 7 > 9$ or $2 + 7 < 9$
Here, connective is or.
It connects two statement $2 + 7 > 9, 2 + 7 < 9.$

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MCQ 1631 Mark

The contrapositive of the statement 'I go to school if it does not rain' is:

A
If it rains, I do not go to school.
✓
If I do not go to school, it rains.
C
If it rains, I go to school.
D
If i go to school, it rains.

Answer

Correct option: B.

If I do not go to school, it rains.

In the given statement, let p denote the part "it does not rain"
Aand q denote the part "i go to school"
So the given statement is $p \rightarrow q$
Now for a contrapositive statement, by definition we have
$(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$
So $\sim q$ means "i do not go to school"
and $\sim p$ means "it rains"
$\sim q \rightarrow \sim p$ means "if i do not go to school, it rains".

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MCQ 1641 Mark

The inverse of the statement "If it is raining then the grass is wet":

✓
"If it is not raining then the grass is not wet".
B
"If it is raining then the grass is not wet".
C
"If it is not raining then the grass is wet".
D
None of these.

Answer

Correct option: A.

"If it is not raining then the grass is not wet".

$p \rightarrow q$
Inverse is $\sim p \rightarrow \sim q$
$\Rightarrow$ Inverse of:
It it is raining then the grass is wet is:
If it is not raining then the grass is not wet.

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MCQ 1651 Mark

$p ∧ (q ∧ r)$ is logically equivalent to.

A
$(p ∨ q) ∧ r$
✓
$(p ∧ q) ∧ r$
C
$p \rightarrow (q ∧ r)$
D
$(p ∨ q) ∨ r$

Answer

Correct option: B.

$(p ∧ q) ∧ r$

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MCQ 1661 Mark

The negation of the Boolean expression $p ∨ (\sim p ∧ q)$ is equivalent to $\sim$

A
$p ∧ \sim q$
✓
$\sim p ∧ \sim q$
C
$\sim p ∨ \sim q$
D
$\sim p ∨ q$

Answer

Correct option: B.

$\sim p ∧ \sim q$

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MCQ 1671 Mark

If $p \Rightarrow (~p ∨ q)$ is false, the truth values of $p$ and $q$ are respectively.

A
$F, T$
B
$F, F$
C
$T, T$
✓
$T, F$

Answer

Correct option: D.

$T, F$

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MCQ 1681 Mark

The contra$-$positive of the statement if $p$ then $q$ is:

A
If $\sim p$ then $q$
B
If $p$ then $\sim q$
C
If $q$ then $p$
✓
If $\sim q$ then $\sim p$

Answer

Correct option: D.

If $\sim q$ then $\sim p$

Given statement is if $p$ then $q$
Now, contra$-$positive of the statement is:
If $\sim q$ then $\sim p$

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MCQ 1691 Mark

If the coefficient of variation is $100$ the mean of the data is $25,$ then find the standard deviation.

A
$5$
B
$10$
C
$15$
✓
$25$

Answer

Correct option: D.

$25$

Coefficient of Variance $ = (\frac{\text{Standard Deviation}}{\text{Mean}}) \times 100$
$ \Rightarrow$ Standard Deviation $= 25.$

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MCQ 1701 Mark

Which of the following statements is the inverse of "If it rains, then I do not go fishing."?

A
If I go fishing, then it does not rain.
B
If I do not go fishing, then it rains.
✓
If it does not rain, then I go fishing.
D
None of these.

Answer

Correct option: C.

If it does not rain, then I go fishing.

Therefore, the reason comes after the assertion.
Then, the inverse of the expression "if it rains, then I do not go fishing " is:
If I go fishing, then it does not rain.

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MCQ 1711 Mark

Choose the correct answer:
The contrapositive of the statement.
“If $7$ is greater than $5$, then $8$ is greater than $6”$ is.

A
If $8$ is greater than $6,$ then $7$ is greater than $5.$
B
If $8$ is not greater than $6,$ then $7$ is greater than $5.$
✓
If $8$ is not greater than $6,$ then $7$ is not greater than $5.$
D
If $8$ is greater than $6$, then $7$ is not greater than $5.$

Answer

Correct option: C.

If $8$ is not greater than $6,$ then $7$ is not greater than $5.$

Letp: $7$ is greater than $5.$
and $q: 8$ is greater than $6.$
$\therefore p \rightarrow q$
$\sim p: 7$ is not greater than $5.$
$\sim q: 8$ is not greater than $6.$
$(\sim q) \rightarrow (\sim p)$ i.e., if $8$ is not greater than $6,$ then $7$ is not greater than $5.$

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MCQ 1721 Mark

If $p$ then $q$ means if $p$ is $...........$ then $q$ must be $...........$

✓
True, true
B
True, false
C
False, false
D
False, true

Answer

Correct option: A.

True, true

If $p$ then $q$ means if $p$ is true then $q$ must be true.
It says nothing when $p$ is false.
If $p$ is false then $q$ might be true or false.

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MCQ 1731 Mark

If $p \rightarrow (~p ∨ ~q)$ is false, then the truth values of $p$ and $q$ are respectively.

A
$T, F$
B
$F, F$
C
$F, T$
✓
$T, T$

Answer

Correct option: D.

$T, T$

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MCQ 1741 Mark

If $p$ then $q$ means if $p$ is $...........$ then $q$ must be $...........$

✓
true, true
B
true, false
C
false, false
D
false, true

Answer

Correct option: A.

true, true

If $p$ then $q$ means if $p$ is true then $q$ must be true.
It says nothing when $p$ is false.
If $p$ is false then q might be true or false.

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MCQ 1751 Mark

Which of the following is the inverse of the proposition: “If a number is a prime then it is odd.”

A
If a number is not a prime then it is odd
✓
If a number is not a prime then it is odd
C
If a number is not odd then it is not a prime
D
If a number is not odd then it is a prime

Answer

Correct option: B.

If a number is not a prime then it is odd

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MCQ 1761 Mark

If $p$ then $q$ means $...........$

A
If $q$ then $p$
✓
$p \Rightarrow q$
C
$q \Rightarrow p$
D
$q$ only if $p$

Answer

Correct option: B.

$p \Rightarrow q$

If $p$ then $q$ means $p$ implies $q$
i.e. $p \Rightarrow q.$
This does not mean $q \Rightarrow p.$
$Q$ only if $p$ means $q \Rightarrow p.$

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MCQ 1771 Mark

Which of the following is not a negation of the statement A natural number is greater than zero.

A
A natural number is not greater than zero
B
It is false that a natural number is greater than zero
✓
It is false that a natural number is not greater than zero
D
None of these

Answer

Correct option: C.

It is false that a natural number is not greater than zero

Given statement is:
A natural number is greater than zero Negation of the statement:
A natural number is not greater than zero
It is false that a natural number is greater than zero

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MCQ 1781 Mark

Which of the following is a statement.

A
$x$ is a real number
B
Switch of the fan
✓
$6$ is a natural number
D
Let me go

Answer

Correct option: C.

$6$ is a natural number

The statement $6$ is a natural number is true.
So, it is a statement.

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MCQ 1791 Mark

Choose the correct answer:
The converse of the statement.
“If sun is not shining, then sky is filled with clouds” is.

✓
If sky is filled with clouds, then the sun is not shining.
B
If sun is shining, then sky is filled with clouds.
C
If sky is clear, then sun is shining.
D
If sun is not shining, then sky is not filled with clouds.

Answer

Correct option: A.

If sky is filled with clouds, then the sun is not shining.

Let $p:$ Sun is not shining.
$q:$ Sky is filled with clouds.
So, the converse of the statement $p \rightarrow q$ is $q \rightarrow p.$
i.e., If Sky is filled with clouds, then the Sun is not shining.

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MCQ 1801 Mark

Which of the following cannot be the negation of the statement “All angles are equal in equilateral triangle”?

A
There is at least one angle different in equilateral triangle.
B
It is false that all angles are equal in equilateral triangle.
C
It is not the case that all angles are equal in equilateral triangle.
✓
All angles are unequal in equilateral triangle.

Answer

Correct option: D.

All angles are unequal in equilateral triangle.

Negation of all angles is ‘not all angles’. So, negation of the given statement is “There is at least one angle different in equilateral triangle”, “It is false that all angles are equal in equilateral triangle”, “It is not the case that all angles are equal in equilateral triangle”. But “All angles are unequal in equilateral triangle” cannot be the negation of given statement as this does not include isosceles triangles.

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M.C.Q (1 Marks) - Page 4 - MATHS STD 11 Science Questions - Vidyadip